The small-scale structure of quantum spacetime

TL;DR

This paper models quantum spacetime as a statistical system of curvature fluctuations obeying thermodynamic principles, deriving Einstein's equations from entropy maximization and suggesting a new perspective on the cosmological constant and zero-point energy.

Contribution

It introduces a background-independent statistical physics framework for quantum spacetime, deriving Einstein's equations from entropy considerations and linking curvature fluctuations to cosmological phenomena.

Findings

Entropy of quantum spacetime is proportional to Einstein-Hilbert action.

Derived equations of motion match Einstein's field equations.

Suggests zero-point energy may not be problematic due to entropy-based formulation.

Abstract

Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since the collection of fluctuations is a many-body system, the natural explanation for their position-independent statistics is that they are in equilibrium with each other and distributed at maximum entropy. Consequently, their probability distributions obey the laws of statistical physics which enforces small-scale smoothness, prevents the homogeneity-violating diffusion found in any free quantum system, and maintains decoherence. Their entropy, calculated using the explicitly-constructed phase space of the Riemann whose statistics are derived using a background-independent graviton exchange ensemble, is proportional to the Einstein-Hilbert action evaluated on the macroscopic expected geometry and includes a small, positive cosmological constant. Entropy maximization yields quantum spacetime's Ehrenfest equations of motion which are identical to Einstein's expectation-valued field equations. This background-independent dynamical formulation reveals curvature fluctuation entropy as a source of expansion and raises the possibility that matter's zero-point energy problem, which is action-based and not energy shift invariant, may not be a problem after all.